Chapter 6: Q. 303 (page 627)

Solve the following exercise
$15 x^{2} - 10 x = 40$

Short Answer

Expert verified

The value of $x = - \frac{4}{3}, x = 2$ .

Step by step solution

Step 1. Given information

The given equation $15 x^{2} - 10 x = 40$ .

Step 2. Simplify the quadratic equation

$Simplify the quadratic expression : 15 x ² - 10 x = 40 [Given the expression] 15 x^{2} - 10 x - 40 = 0 [Write the quadratic equation of standard form] 5 (3 x^{2} - 2 x - 8) = 0 [Factor out 3 from expression] 5 (31 ² - 6 x + 4 x - 8) = 0 [since; - 6 x = - 6 . x + 4 x] 5 (3 x * (x - 2) + 4 (x - 2)) = 0 [Factor out the common factor from group] 5 (3 x + 4) * (x - 2) = 0 [Factor the common factor from expression] 5 - 0 o r 3 x + 4 = 0 o r x - 2 = 0 [Use the zero product property] or x = - \frac{4}{3} or x = 2$

(a - b) (a + b) = 0 a - b = 0 or a + b = 0 a = b or a = - b

Step 3. Checking the roots

$Check : Substitute the value x = - 4 / 3 in the original equation . 15 x^{2} - 10 x = 4 ([Given equation) 15 * (- \frac{4}{3})^{2} - 10 (- \frac{4}{3}) = 40] [Put x = - \frac{4}{3}] \frac{80}{3} + \frac{40}{3} = 40 40 = 40 T r u e Substitute the value x = 2 in the original equation . 15 x^{2} - 10 x = 40 [Given equation] 15 \times (2)^{2} - 10 (2) = 40 [Put x = 2] 60 - 20 = 40 40 = 40 Therefore, answer is x = - 4 / 3, x = 2$

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Solve the following exercise
$15 x^{2} - 10 x = 40$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the quadratic equation

Step 3. Checking the roots

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Solve the following exercise15x2-10x=40

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the quadratic equation

Step 3. Checking the roots

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Statistics

Mechanics Maths

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve the following exercise
$15 x^{2} - 10 x = 40$